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On a bivariate Pólya-Aeppli distribution. (English) Zbl 1307.60006
Summary: In this article, we use the bivariate Poisson distribution obtained by the trivariate reduction method and compound it with a geometric distribution to derive a bivariate Pólya-Aeppli distribution. We then discuss a number of properties of this distribution including the probability generating function, correlation structure, probability mass function, recursive relations, and conditional distributions. The generating function of the tail probabilities is also obtained. Moment estimation of the parameters is then discussed and illustrated with a numerical example.

MSC:
60E05 Probability distributions: general theory
62P05 Applications of statistics to actuarial sciences and financial mathematics
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